Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
143 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11716837 | C2 | semidirect |
| 3. D5⋊#672 | C2 | semidirect |
| 6. C52×D8 | C4 | semidirect |
| 8. C5×D40 | C4 | semidirect |
| 41. C5×D8 | Dic5 | semidirect |
| 42. C5×D8 | AGL(1,𝔽5) | semidirect |
| 46. D40 | Dic5 | semidirect |
| 77. C52 | #357 | semidirect |
| 99. D8 | #1042 | semidirect |
| 124. C5 | #64782 | semidirect |
| 125. C5 | #64904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×D8 | 2 |
| #11716837 | 2 |
| D5⋊#672 | 2 |
| #64904 | 5 |
| #64782 | 5 |